Born in Thompson, Manitoba, Leschyshyn was a junior standout with the WHL's Saskatoon Blades. He was taken third overall by the Quebec Nordiques in the 1988 NHL Entry Draft and became a pillar on the club's defence through some very lean years. He remained a valuable member of the club when it improved after the trading of 1991 First round draft pick, Eric Lindros in 1992.
Leschyshyn remained with the franchise when it relocated to Colorado in 1995-96 and was part of the Stanley Cup celebrations that spring. After the 1996 Stanley Cup victory, the veteran backliner started to become a journeyman. He played a week in Washington then was shipped to the Hartford Whalers for Andrei Nikolishin.
The solid defenceman remained with the franchise when it relocated to Carolina in 1997-98. Leschyshyn was claimed by the Minnesota Wild in the 2000 Expansion Draft where he provided stability and leadership on the young club. Prior to the March deadline he was sent to the Ottawa Senators to add depth to their blueline and has continued his steady play.
During the 2003-04 season, the former first rounder played his 1,000th NHL game and in the summer of 2005 was acquired by the Colorado Avalanche. After taking part in training camp, Leschyshyn announced his retirement a few days prior to the opening of the 2005-06 season.